Algebraic Thinking Habits

Lesson 1: Doing and Undoing

Lesson Objectives

• Learn About the Doing and Undoing Algebraic Thinking Habit.

• Learn How to Use a Cognitive Strategy to Calculate the Percentage of a Whole Number.

• Learn How to Use Division and Multiplication to Calculate a Missing Value.

The 3 Major Algebraic Thinking Habits

• Doing-Undoing• Building Rules to Represent Functions• Abstracting from Computation

(Driscoll,1999)

Doing and Undoing

• In this brief lesson we will focus on the doing and undoing algebraic thinking habit. We will use this algebraic thinking habit to answer questions concerning percentages.

• Doing-Undoing: Effective algebraic thinking sometimes involves reversibility (i.e., being able to undo mathematical processes as well as do them). In effect, it is the capacity not only to use a process to get to a goal, but also to understand the process well enough to work backward from the answer to the starting point (Driscoll, 1999).

WAIT

Let’s Take a Look At a Cognitive Strategy First

What is a Cognitive Strategy?

Cognitive strategies are techniques that learners use to optimize their cognitive processes (Smith & Ragan, 2005).

Breaking Whole Numbers Into Percentages

• 10% of any whole number can be mentally calculated by simply moving the decimal point one place to the left. This can be done one additional time to break the whole number down to 1%.

Breaking Whole Numbers Down Into Percentages (Continued).

• These numbers can then be multiplied to determine the percentage amount.

46% of 250=

(25 X 4) + (2.5 X 6) = 107.5

Building Percentages Up Into Whole Numbers

• Sometimes You May Have a Percentage and Need to Find Out The Whole Number.

• EX: 20 is 30% of what number?

• You can simply divide 20 by 30 and move the decimal two places to the RIGHT.

Practice

• What is 25% of 700? (Try to calculate without a calculator).

Practice

Did you get 147?

Next

Watch the “House for Sale” animation and try to answer the questions at the end.

Summary

• Doing-Undoing: Effective algebraic thinking sometimes involves reversibility (i.e., being able to undo mathematical processes as well as do them). In effect, it is the capacity not only to use a process to get to a goal, but also to understand the process well enough to work backward from the answer to the starting point (Driscoll, 1999).

• Cognitive strategies are techniques that learners use to optimize their cognitive processes (Smith & Ragan, 2005).

THE END